Sounds like anarcho-capitalism to me. It's basically the purest form of capitalism the same as communism is the purest form of socialism. The problem with both is that they rely on people being inherently good, which they are not. You have been complaining that the government kills people but you have forgotten that the government is made up of the same people that you say will work together in the absence of it.
Further, your claim that to punish murderers all we have to do is not give them goods or services is bogus. If we live in a purely free society as you wish, then what would stop me if I choose to sell to murderers? The only thing that you have said there is that people won't want to give goods and services to murderers because of some societal moral code. But do you know what always trumps morals? Money. If no one is selling to murderers or rapists then that right there is an untapped market. I could capitalize on that market by selling exclusively to only murderers and rapists so while everyone is splitting the market with the good people, I would have a larger slice of the bad folks. And I would be relatively safe from being attacked by these people because if I am the only one selling to them then they need me as much as I need them.
Further, your claim that to punish murderers all we have to do is not give them goods or services is bogus. If we live in a purely free society as you wish, then what would stop me if I choose to sell to murderers? The only thing that you have said there is that people won't want to give goods and services to murderers because of some societal moral code. But do you know what always trumps morals? Money. If no one is selling to murderers or rapists then that right there is an untapped market. I could capitalize on that market by selling exclusively to only murderers and rapists so while everyone is splitting the market with the good people, I would have a larger slice of the bad folks. And I would be relatively safe from being attacked by these people because if I am the only one selling to them then they need me as much as I need them.